Problem: Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on $3$ trips, and for each trip Lennox gets $300$ dollars. On a single trip, a truck delivers $50$ packs, and each pack contains $12$ kilograms of apples. Overall, Lennox sells $4500$ dollars worth of apples in a week. How many trucks are in Lennox's fleet?
Answer: There can be many ways to solve this problem. Here, we will do this by thinking about units. Let's say there are $x\,\text{trucks}$ in Lennox's fleet. We are given that Lennox makes a total of $4500\,\text{dollars}$ each week. How can we relate these two quantities with an equation? $\begin{aligned} x\,\text{trucks}\cdot y\,\dfrac{\text{dollars}}{\text{truck}}=4500\,\text{dollars} \end{aligned}$ So in order to find the number of trucks $x$, we need to figure out the value of $y$, which is the rate of dollars per truck. Notice what other information we are given: $3\,\dfrac{\text{trips}}{\text{truck}}$ $300\,\dfrac{\text{dollars}}{\text{trip}}$ $50\,\dfrac{\text{packs}}{\text{trip}}$ $12\,\dfrac{\text{kilograms}}{\text{pack}}$ Which of these quantities can help us calculate a rate whose units are $\dfrac{\text{dollars}}{\text{truck}}$ ? We can combine the following quantities: $\begin{aligned} 3\,\dfrac{\cancel\text{trips}}{\text{truck}}\cdot 300\,\dfrac{\text{dollars}}{\cancel\text{trip}}=900\,\dfrac{\text{dollars}}{\text{truck}} \end{aligned}$ Now we can plug that in the original equation: $\begin{aligned} x\,\text{trucks}\cdot 900\,\dfrac{\text{dollars}}{\text{truck}}&=4500\,\text{dollars} \\\\ x\,\text{trucks}&=\dfrac{4500}{900}\,\cancel\text{dollars}\cdot\dfrac{\text{trucks}}{\cancel\text{dollar}} \\\\ x\,\text{trucks}&=5\,\text{trucks}\end{aligned}$ In conclusion, Lennox's fleet has $5$ trucks.